31,387 research outputs found
Noise-Resilient Group Testing: Limitations and Constructions
We study combinatorial group testing schemes for learning -sparse Boolean
vectors using highly unreliable disjunctive measurements. We consider an
adversarial noise model that only limits the number of false observations, and
show that any noise-resilient scheme in this model can only approximately
reconstruct the sparse vector. On the positive side, we take this barrier to
our advantage and show that approximate reconstruction (within a satisfactory
degree of approximation) allows us to break the information theoretic lower
bound of that is known for exact reconstruction of
-sparse vectors of length via non-adaptive measurements, by a
multiplicative factor .
Specifically, we give simple randomized constructions of non-adaptive
measurement schemes, with measurements, that allow efficient
reconstruction of -sparse vectors up to false positives even in the
presence of false positives and false negatives within the
measurement outcomes, for any constant . We show that, information
theoretically, none of these parameters can be substantially improved without
dramatically affecting the others. Furthermore, we obtain several explicit
constructions, in particular one matching the randomized trade-off but using measurements. We also obtain explicit constructions
that allow fast reconstruction in time \poly(m), which would be sublinear in
for sufficiently sparse vectors. The main tool used in our construction is
the list-decoding view of randomness condensers and extractors.Comment: Full version. A preliminary summary of this work appears (under the
same title) in proceedings of the 17th International Symposium on
Fundamentals of Computation Theory (FCT 2009
Sufficient condition on noise correlations for scalable quantum computing
I study the effectiveness of fault-tolerant quantum computation against
correlated Hamiltonian noise, and derive a sufficient condition for
scalability. Arbitrarily long quantum computations can be executed reliably
provided that noise terms acting collectively on k system qubits are
sufficiently weak, and decay sufficiently rapidly with increasing k and with
increasing spatial separation of the qubits.Comment: 13 pages, 1 figure. (v2) Minor corrections and clarification
Stochastically Resilient Observer Design for a Class of Continuous-Time Nonlinear Systems
This work addresses the design of stochastically resilient or non-fragile continuous-time Luenberger observers for systems with incrementally conic nonlinearities. Such designs maintain the convergence and/or performance when the observer gain is erroneously implemented due possibly to computational errors i.e. round off errors in computing the observer gain or changes in the observer parameters during operation. The error in the observer gain is modeled as a random process and a common linear matrix inequality formulation is presented to address the stochastically resilient observer design problem for a variety of performance criteria. Numerical examples are given to illustrate the theoretical results
Error-Correcting Data Structures
We study data structures in the presence of adversarial noise. We want to
encode a given object in a succinct data structure that enables us to
efficiently answer specific queries about the object, even if the data
structure has been corrupted by a constant fraction of errors. This new model
is the common generalization of (static) data structures and locally decodable
error-correcting codes. The main issue is the tradeoff between the space used
by the data structure and the time (number of probes) needed to answer a query
about the encoded object. We prove a number of upper and lower bounds on
various natural error-correcting data structure problems. In particular, we
show that the optimal length of error-correcting data structures for the
Membership problem (where we want to store subsets of size s from a universe of
size n) is closely related to the optimal length of locally decodable codes for
s-bit strings.Comment: 15 pages LaTeX; an abridged version will appear in the Proceedings of
the STACS 2009 conferenc
An exploration of feature detector performance in the thermal-infrared modality
Thermal-infrared images have superior statistical properties compared with visible-spectrum images in many low-light or no-light scenarios. However, a detailed understanding of feature detector performance in the thermal modality lags behind that of the visible modality. To address this, the first comprehensive study on feature detector performance on thermal-infrared images is conducted. A dataset is presented which explores a total of ten different environments with a range of statistical properties. An investigation is conducted into the effects of several digital and physical image transformations on detector repeatability in these environments. The effect of non-uniformity noise, unique to the thermal modality, is analyzed. The accumulation of sensor non-uniformities beyond the minimum possible level was found to have only a small negative effect. A limiting of feature counts was found to improve the repeatability performance of several detectors. Most other image transformations had predictable effects on feature stability. The best-performing detector varied considerably depending on the nature of the scene and the test
Approximate resilience, monotonicity, and the complexity of agnostic learning
A function is -resilient if all its Fourier coefficients of degree at
most are zero, i.e., is uncorrelated with all low-degree parities. We
study the notion of of Boolean
functions, where we say that is -approximately -resilient if
is -close to a -valued -resilient function in
distance. We show that approximate resilience essentially characterizes the
complexity of agnostic learning of a concept class over the uniform
distribution. Roughly speaking, if all functions in a class are far from
being -resilient then can be learned agnostically in time and
conversely, if contains a function close to being -resilient then
agnostic learning of in the statistical query (SQ) framework of Kearns has
complexity of at least . This characterization is based on the
duality between approximation by degree- polynomials and
approximate -resilience that we establish. In particular, it implies that
approximation by low-degree polynomials, known to be sufficient for
agnostic learning over product distributions, is in fact necessary.
Focusing on monotone Boolean functions, we exhibit the existence of
near-optimal -approximately
-resilient monotone functions for all
. Prior to our work, it was conceivable even that every monotone
function is -far from any -resilient function. Furthermore, we
construct simple, explicit monotone functions based on and that are close to highly resilient functions. Our constructions are
based on a fairly general resilience analysis and amplification. These
structural results, together with the characterization, imply nearly optimal
lower bounds for agnostic learning of monotone juntas
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